Registry entries. Lots of them. And some configuration files.
Those are all on the PC that the application is installed on. Since the other PC doesn't have these entries, the program is essentially missing critical components, and it won't run. Tracking down and duplicating all the registry entries (probably thousands of them) would be next to impossible, plus you would have to edit some path names to reflect the network folder path, instead of C:\Program Files\Microsoft Office, or whatever the case may be.
This is the same reason that for a lot of programs now, you can't just copy and paste the Program Files\Whatever-program folder into another PC and load it up. It'll look for the registry entries, be unable to find them, and freak out.
Sharing folders is mainly for the data files - documents, images, audio, video, databases, and more. Each user wanting the data files must have the appropriate viewers or editors (Office in this case) installed on their respective PC's.